A lossless reversible coding method is a known method of compressing audio, visual or other information. In applications where a waveform is directly recorded as a linear PCM signal, various compression coding methods have been proposed (see Non-patent literature 1, for example). For example, a prediction coding method, such as MPEG-4 ALS, is known (see Non-patent literature 2, for example). The prediction coding method is to code a prediction error reduced in amplitude by linear prediction and a linear prediction coefficient.
In long-distance telephone transmission or audio transmission for Voice over Internet Protocol (VoIP), the near-logarithmic companded PCM standardized under ITU-T G.711, which uses 8 bits for each sample, is used instead of the linear PCM, which directly uses the numerical values of the amplitude. If the VoIP system becomes more popular than the ordinary telephone system, the required transmission capacity will increase, so that the demand for a lossless compression coding method based on the near-logarithmic companded PCM will also increase. In the VoIP system, the length of a frame, which is a unit of compression, is short in order to reduce the delay time, and each frame may be composed of 40 samples.